Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+4y &= 2 \\ 6x+4y &= -1\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $4y = -6x-1$ Divide both sides by $4$ to isolate $y$ $y = {-\dfrac{3}{2}x - \dfrac{1}{4}}$ Substitute this expression for $y$ in the first equation. $2x+4({-\dfrac{3}{2}x - \dfrac{1}{4}}) = 2$ $2x - 6x - 1 = 2$ Simplify by combining terms, then solve for $x$ $-4x - 1 = 2$ $-4x = 3$ $x = -\dfrac{3}{4}$ Substitute $-\dfrac{3}{4}$ for $x$ back into the top equation. $2( -\dfrac{3}{4})+4y = 2$ $-\dfrac{3}{2}+4y = 2$ $4y = \dfrac{7}{2}$ $y = \dfrac{7}{8}$ The solution is $\enspace x = -\dfrac{3}{4}, \enspace y = \dfrac{7}{8}$.